lesson 8-2 parallelograms
DESCRIPTION
Lesson 8-2 Parallelograms. Theorem 8.3 Opposite sides of a parallelogram are congruent Theorem 8.4 Opposite angles in a parallelogram are congruent Theorem 8.5 Consecutive angles in a parallelogram are supplementary. Theorems ( con’t ). Theorem 8.6 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/1.jpg)
Lesson 8-2 Parallelograms
• Theorem 8.3Opposite sides of a parallelogram are congruent• Theorem 8.4Opposite angles in a parallelogram are
congruent• Theorem 8.5Consecutive angles in a parallelogram are
supplementary
![Page 2: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/2.jpg)
Theorems (con’t)
• Theorem 8.6If a parallelogram has one right angle, it has four
right angles• Theorem 8.7The diagonals of a parallelogram bisect each other• Theorem 8.8Each diagonal of a parallelogram separates the
parallelogram into two congruent triangles.
![Page 3: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/3.jpg)
Prove that if a parallelogram has two consecutive sides congruent, it has four sides congruent.
Given:
Prove:
![Page 4: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/4.jpg)
1. 1. Given
Proof:
ReasonsStatements
4. Transitive Property4.
2. Given2.
3. Opposite sides of a parallelogram are .
3.
![Page 5: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/5.jpg)
Given:
Prove:
Prove that if and are the diagonals of , and
![Page 6: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/6.jpg)
Proof:
ReasonsStatements
1. Given1.
4. Angle-Side-Angle4.
2. Opposite sides of a parallelogram are congruent.
2.
3. If 2 lines are cut by a transversal, alternate interior s are .
3.
![Page 7: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/7.jpg)
If lines are cut by a transversal, alt. int.
Definition of congruent angles
Substitution
RSTU is a parallelogram. Find and y.
![Page 8: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/8.jpg)
Angle Addition Theorem
Substitution
Subtract 58 from each side.
![Page 9: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/9.jpg)
Substitution
Divide each side by 3.
Definition of congruent segments
Answer:
![Page 10: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/10.jpg)
ABCD is a parallelogram.
Answer:
![Page 11: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/11.jpg)
Read the Test ItemSince the diagonals of a parallelogram bisect each other, the intersection point is the midpoint of
A B C D
MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram MNPR, with vertices M(–3, 0), N(–1, 3), P(5, 4), and R(3, 1)?
![Page 12: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/12.jpg)
Solve the Test Item
Find the midpoint of
The coordinates of the intersection of the diagonals of parallelogram MNPR are (1, 2).
Answer: C
Midpoint Formula
![Page 13: Lesson 8-2 Parallelograms](https://reader034.vdocuments.us/reader034/viewer/2022042718/568139f0550346895da1a9b1/html5/thumbnails/13.jpg)
Answer: B
A B C D
MULTIPLE-CHOICE TEST ITEM What are the coordinates of the intersection of the diagonals of parallelogram LMNO, with verticesL(0, –3), M(–2, 1), N(1, 5), O(3, 1)?